Skip to Main Content
Frequently Asked Questions
Submit an ETD
Global Search Box
Need Help?
Keyword Search
Participating Institutions
Advanced Search
School Logo
Files
File List
Zhuang HE Thesis.pdf (358.92 KB)
ETD Abstract Container
Abstract Header
On Moduli Spaces of Weighted Pointed Stable Curves and Applications
Author Info
He, Zhuang
Permalink:
http://rave.ohiolink.edu/etdc/view?acc_num=osu1437187765
Abstract Details
Year and Degree
2015, Master of Science, Ohio State University, Mathematics.
Abstract
Moduli spaces of curves have been central objects for decades in algebraic geometry. This paper reviews a generalization by Hassett in 2003 of the classic moduli problem. Hassett's moduli spaces classify the stable n-pointed curves of given genus g, with weighted data on the marked points. Hassett proved the existence of such coarse moduli spaces as projective schemes. In the first chapters we review the classic moduli problems and provide a sketch of GIT construction of moduli spaces. Then we review the reductions maps between moduli space of weighted pointed stable curves. Next we discuss the chamber decomposition and wall crossing maps among our moduli spaces. The last sections provided an exposition of the application to several birational constructions of moduli spaces. We review Kapranov, Keel, and Losev-Manin's examples, and discuss the realizations of their examples by successive reductions between weighted pointed moduli spaces.
Committee
Hsian-Hua Tseng (Advisor)
Jean-François Lafont (Committee Member)
Pages
57 p.
Subject Headings
Mathematics
Keywords
Moduli Spaces
;
Algebraic Geometry
;
Birational Geometry
;
Geometric Invariant Theory
;
Stacks
;
Recommended Citations
Refworks
EndNote
RIS
Mendeley
Citations
He, Z. (2015).
On Moduli Spaces of Weighted Pointed Stable Curves and Applications
[Master's thesis, Ohio State University]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=osu1437187765
APA Style (7th edition)
He, Zhuang.
On Moduli Spaces of Weighted Pointed Stable Curves and Applications.
2015. Ohio State University, Master's thesis.
OhioLINK Electronic Theses and Dissertations Center
, http://rave.ohiolink.edu/etdc/view?acc_num=osu1437187765.
MLA Style (8th edition)
He, Zhuang. "On Moduli Spaces of Weighted Pointed Stable Curves and Applications." Master's thesis, Ohio State University, 2015. http://rave.ohiolink.edu/etdc/view?acc_num=osu1437187765
Chicago Manual of Style (17th edition)
Abstract Footer
Document number:
osu1437187765
Download Count:
780
Copyright Info
© 2015, some rights reserved.
On Moduli Spaces of Weighted Pointed Stable Curves and Applications by Zhuang He is licensed under a Creative Commons Attribution-NonCommercial-NoDerivs 3.0 Unported License. Based on a work at etd.ohiolink.edu.
This open access ETD is published by The Ohio State University and OhioLINK.